PSG were expected to offer €90m for the Croatia international this week.
But after victory at Rayo, Rakitic stated: "I have had a few days to reflect a little, talk over different things, I have had four fantastic years here and I would like to stay here a long time.
"To be part of the best club in the world is as good as it gets. I speak with my wife and my representative Arturo, and there is no place where I would be better off.
"There were several clubs that enquired about me. We spoke about everything and now the decision is final. The most important thing is that I want to be here, I feel privileged to be in the best club in the world."